- PRESSURE DISTRIBUTIONS, AND
6. AEROFOIL RAE 2 8 2 2
BOUNDARY LAYER AND WAKE MEASUREMENTS
by
P. H. Cook, M. A. McDonald and M. C. P. Firmin
Royal Aircraft Establishment. Farnbarough, Hants, United Kingdom
I. INTRODUCTION
The examples presented have been selected to give a range of conditions from wholly subcritical flow
to conditions where a comparatively strong shock wave exists in the flow above the upper surface of the
aerofoil. In at least one example some boundary layer separation occurs due to the shock wave but reattach-
ment occurs ahead of the trailing edge of the aerofoil.
The data include surface pressure measurements and mean flow boundary layer and wake profiles deduced
fromtraversesof pitot and static pressure measuring probes. Where the measurements have been made close
to the aerofoil (ie xlc r 1.025) the probes have been mounted from within the model, thus keeping the
probe support interference to a minimum.
In all examples presented, attempts have been made to fix boundary-layer transition near to the lead-
ing edge af the aerofoil (xlc = 0.03 or xlc = O.11), but as the measurements were made for a range of
Reynolds numbers and Mach numbers, in some cases without changing the transition trip, the roughness size
may be larger than would normally be used at the higher Reynolds numbers. In some examples the presence
of the roughness has clearly had a strong local effect on the pressure distribution. The local disturbance
to the boundary layers has not been measured but the downstream developments, of course, include the
influence of the trip.
In parts of the flow the normal boundary-layer assumptions are violated by the normal pressure
gradients which are significant near the trailing edge of the aerofoil and in the region of a shock wave.
Ideally it is necessary to take account of the normal pressure gradients in defining the boundary layer
integral parameters and in one example the data are presented with and without allowance for the normal
pressure gradients (Case 9 - configurations CI and C2 respectively). Where boundary layers are measured
downstream of a shock wavethe total pressure measured by the pitot tube is affected by the total head loss
due to the shock wave. However the edge of the boundary layer was usually well defined. For traverses
made in the near wake the measurements have been treated as two separate boundary layers, without extra-
polation to a surface but with the division between the two parts taken at the point of minimum velocity
ratio. Examples are given of traverses made well behind the trailing edge of the aerofoil the purpose of
which has been to determine the total drag. Consequently the traverse has included as far as possible the
complete region behind the shock wave as well as the viscous wake. The definition of momentum thickness
is then different from that used for the boundary layers where shock losses outside the viscous layer are
excluded.
In the data reduction it has been assumed that the flow is two-dimensional, and so the surface
pressure distribution measured near the centre section of the aerofoil (see Fig 6.4) has been used in
nearly all cases as the value of the static pressure at the aerofoil surface for determining the velocity
profiles and any variation of the static pressure within a profile is only taken into account if actual
measurements exist. The variation of the static pressure through the boundary layer andlor wake has
normally been obtained from a traverse at one spanwise station and used at others. Although for the main
part of the data this assumption is satisfactory, there are c a s e s , for instance when the boundary layer is
close to separation, where a significant difference may exist. The data presented in the tables have as
far as possible been presented so that re-analysis is possible by the reader.
2. BOUNDARY LAYER AND WAKE ANALYSIS
2.1 Measured profiles
The local Mach number (M,,), within the boundary layer or wake, has been obtained from values of
total pressure (P ) and static pressure (P ) at the measurement point from the equation
0 L
When ML S 1 then Po = Po
M
.
the measured value of the pitot pressure, and ML can be obtained directly.
When ML > I then PO # POM and is given by
Thus for ML ,
1 equations (I) and (2) were solved by iteration. Where the variation of static pressure
has not been measured at the appropriate xlc location, the static pressure is assumed to be constant
through the layer. The static pressure used in determining the local conditions is quoted for each point
or profile as appropriate.
The experimental values for 6* and 9 were then obtained by numerical integration of Eq.(8) and (9)
using Eq.(lO) and (11). As described in the next section analytic expressions were used to extend the
profiles to the wall fram the measured point nearest to the wall.
2.3 Extrapolation of the measured profiles to the surface
The extrapolation is based on the logarithmic form of the velocity profiles given by Winter and
~ a u d e t 3and the corresponding equation for the viscous sublayer,
These equations are modified slightly, 6 0 that they are written in terms of the local skin friction
coefficient, and in terms of quantities measured in the experiments as follows
where
and Re is the Reynolds number for the experiments and based on the aerofoil chord and T is the
corresponding stagnation temperature in K . 0
From the values of u/Up deduced previously it is possible using Eq.(14) to obtain an apparent skin
friction coefficient (Cf) as a function of height above the aerofoil surface, which can then be used to
extrapolate the profile to the aerofoil surface using in addition the profile for the viscous sublayer as
given in Eq.(15). In practice a mean value has been obtained for the skin friction coefficient by
averaging the values obtained for all measured points with "/Up r 0.6 or, where there are less than
three points meeting this condition, by averaging the values for the three points closest to the surface.
The spread of values used is indicated by the vertical bars in Fig 6.6 with the symbol indicating the
value used in the extrapolation to the surface*. The profile is assumed to change to the form of the
viscous sublayer at the point where the two equations intersect, ie
A check was made to see that measurements were not used in the extrapolation procedure if they were
within the sublayer thickness of the surface. This did not occur unless the boundary layer was close to
separation.
The contributions to the displacement and momentum thicknesses fram the first measured point to the
surface were then obtained by numerical integration using Eq.(14) and (15), with Eq.(3) and (4) ta derive
the densitv ratio.
* Near the trailing edge, the larger height of the vertical bar is caused by the boundary layer not
obeying the law of the wall form up to u/U = 0.6 , as the boundary layer approaches separation.
P
3. DATA SET
I. Aerofoil
1.1 Aerofoil designation RAE 2822
1.2 Type of a e r o f o i l r e a r - l o a d e d , s u b c r i t i c a l , roof-top type p r e s s u r e
d i s t r i b u t i o n a t d e s i g n c o n d i t i o n s . Designed by
second o r d e r method given i n Ref 4
1.2.1 a e r o f o i l geometry see Fig 6 . 1 and Table 6.1
nose r a d i u s 0 . 0 0 8 2 7 chord
maximum t h i c k n e s s 0 . 1 2 1 chard
base thickness 0
1.2.2 design condition M_ = 0 . 6 6 , CL = 0.56 ( a = 1.06')
design pressure d i s t r i b u t i o n see Fig 6 . 2 and Ref 5
1.3 A d d i t i o n a l remarks c h a r a c t e r i s t i c s of a e r o f o i l s e c t i o n are d e s c r i b e d i n
Ref 5
2. Model geometry
2.1 Chord l e n g t h 0.61 m
2.2 Span (exposed) 1.83 m
2.3 Actual model co-ordinates and see Table 6 . 1
accuracy
2.4 Maximum t h i c k n e s s
2.5 Base t h i c k n e a s
3. Wind t u n n e l (Test c o n d i t i o n s i n b r a c k e t s )
3.1 Designation RAE 8 f r x 6 f t t r a n s o n i c wind t u n n e l
3.2 Type of t u n n e l continuous, closed c i r c u i t
3.2.1 stagnation pressure 10 t o 355 kN/m2 ( 3 6 t o 100 kN/m2)
3.2.2 s t a g n a t i o n temperature 290 t o 323 K ( 3 0 8 t o 323 K)
3.2.3 humidity ' 0 . 0 0 3 a b e o l u t e humidity
3.3 Test section
3.3.1 dimensions height - 1 . 8 3 m, w i d t h
c o r n e r f i l l e t s 160.5 mm
- x
2 . 4 3 m, r e c t a n g u l a r w i t h
45'
3.3.2 type of w a l l s 1 . 6 % s l o t t e d s i d e - w a l l s having 5 s l o t s 5 . 8 4 m wide
a t 353 m c e n t r e s symmetrical about t h e c e n t r e l i n e
of each w a l l , s o l i d roof and f l o o r , l a r g e volume
s i n g l e plenum chamber
3.4 Flow f i e l d
(empty t e s t s e c t i o n )
3.4.1 reference s t a t i c pressure plenum chamber
3.4.2 flow a n g u l a r i t y ~ 0 . 0 3i n~ t h e i n c i d e n c e p l a n e
A0.125O i n t h e p l a n e normal t o t h e i n c i d e n c e p l a n e
3.4.3 Mach number d i s t r i b u t i o n AM < ?0.001 on t h e c e n t r e l i n e i n t h e r e g i o n 0 . 7 5 m
upstream t o 1 . 2 5 m downstream of 0 . 2 5 ~f o r
3.4.4 pressure gradient 0.3 < M < 0.8
3.4.5 turbulence/noise l e v e l see F i g 6 . 3 (from Ref 6 )
3.4.6 r o o f l f l o o r boundary l a y e r n o t measured, approximately 4% t o 5% of t h e t e s t
s e c t i o n semi-height a t t h e model, no s p e c i a l
treatment
4. -
Tests
4.1 Type of measurements surface pressures
wake p i t o t and s t a t i c p r e s s u r e s
boundary l a y e r p i t o t and s t a t i c p r e s s u r e s
o i l f l o w d e t e r m i n a t i o n of flow s e p a r a t i o n s
